I'm assuming by top 20 you're referring to US N&WR rankings and that you literally mean "top 20"...
I'm gonna go out on a limb here but I think for these schools you need:
Honors/>90% in Medicine clerkship and any one of the following: 1)AOA 2)230+ boards 3)research and pubs 4)world traveler or life changing experience
I bet everyone in the IM match this year with 230+ and AOA is applying to these schools. It's probably ok to apply with one or the other BUT...you're applying with neither of these AND no research. Uphill battle my friend, but you have nothing to lose by applying. BTW, I'd part on the left if I were you...scientifically proven to make men more desirable by 3.4%.
I think the best answer is 0% if you decide not to apply to Top 20 programs and X% if you do apply. That can be the only correct answer. Truth is, you never know what your chances are and the best way to find out is if you just go for it. If it is financially feasible then I suggest you do it, don't rule yourself out beforehand. AOA, Honours in Medicine, Research and top notch board scores are important but does that guarentee you an interview spot? My guess is no. Does not having these guarentee that you won't get a an interview spot? No again. I totally agree with Black N'Decker that it may be uphill but who knows. I think you should also talk to your program director. Program Directors worth their weight should know a lot about other rpograms and how they usually feel about candidates. They usually know each other (or they should). Also look at last year's match list to see where your fellow students went. My med school is good but no Harvard etc but we have a few students placed at Stanford and BID and they really like the students they get from our school. Our OB dept loved the students they got from Oregon so now all future applicants from that school gets closely looked at. Of course this can work against you if the previous student was an @ss. So bottom line just go for it!!! and Good luck!!!
Too many variables, but from a top 5 medical school its very likely your home program as well as programs that tend to take a lot of people from your school (which I imagine would be top 20 programs) would be very viable. But hard to say without more info.